Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
A rational cubic spline with tension
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
High-order approximation of conic sections by quadratic splines
Computer Aided Geometric Design
C-curves: an extension of cubic curves
Computer Aided Geometric Design
An O(h2n) Hermite approximation for conic sections
Computer Aided Geometric Design
Two different forms of C-B-splines
Computer Aided Geometric Design
Circular arc approximation by quintic polynomial curves
Computer Aided Geometric Design
G3 approximation of conic sections by quintic polynomial curves
Computer Aided Geometric Design
Local Control of Bias and Tension in Beta-splines
ACM Transactions on Graphics (TOG)
NURBS for Curve and Surface Design
NURBS for Curve and Surface Design
Quadratic trigonometric polynomial curves with a shape parameter
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
A class of algebraic-trigonometric blended splines
Journal of Computational and Applied Mathematics
A class of general quartic spline curves with shape parameters
Computer Aided Geometric Design
Curves and Surfaces Construction Based on New Basis with Exponential Functions
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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Piecewise quartic polynomial curves with a local shape parameter are presented in this paper. The given blending function is an extension of the cubic uniform B-splines. The changes of a local shape parameter will only change two curve segments. With the increase of the value of a shape parameter, the curves approach a corresponding control point. The given curves possess satisfying shape-preserving properties. The given curve can also be used to interpolate locally the control points with GC2 continuity. Thus, the given curves unify the representation of the curves for interpolating and approximating the control polygon. As an application, the piecewise polynomial curves can intersect an ellipse at different knot values by choosing the value of the shape parameter. The given curve can approximate an ellipse from the both sides and can then yield a tight envelope for an ellipse. Some computing examples for curve design are given.